Introduction to the LASSO

The term ‘high-dimensional’ refers to the case where the number of unknown parameters to be estimated, p, is of much larger order than the number of observations, n, that is p ≫ n. Since traditional statistical methods assume many observations and a few unknown variables, they can not cope up with t...

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Bibliographic Details
Published in:Resonance 2018-01, Vol.23 (4), p.439-464
Main Author: Gauraha, Niharika
Format: Article
Language:English
Subjects:
Quadratic programming
Regression analysis
Statistical methods
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Summary:The term ‘high-dimensional’ refers to the case where the number of unknown parameters to be estimated, p, is of much larger order than the number of observations, n, that is p ≫ n. Since traditional statistical methods assume many observations and a few unknown variables, they can not cope up with the situations when p ≫ n. In this article, we study a statistical method, called the ‘Least Absolute Shrinkage and Selection Operator’ (LASSO), that has got much attention in solving high-dimensional problems. In particular, we consider the LASSO for high-dimensional linear regression models. We aim to provide an introduction of the LASSO method as a constrained quadratic programming problem, and we discuss the convex optimization based approach to solve the LASSO problem. We also illustrate applications of LASSO method using a simulated and a real data examples.
ISSN:0971-8044
0973-712X
DOI:10.1007/s12045-018-0635-x